topic 4 cost benefit analysis (with page 41)

8/9/2019 Topic 4 Cost Benefit Analysis (With Page 41)

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Cost-BenefitAnalysisEC3351 Topic 4


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Cost-Benefit Analysis

Cost-Benefit Analysis (CBA) = measurement,estimation and comparison of a project’s costsand benefits

General decision rules:

• A project should be undertaken if its benefit

exceeds its cost• The scale of the project should be increased as

long as MB > MC

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CBA of Government Projects

A private sector firm considers the costs and

benefits to itself

A government considers the costs and benefits

to everyone in society

•

Not just costs and benefits that accrue togovernment itself!

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An expressway project

A city

government is

planning an

infrastructureproject:

A North South

Expressway

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Costs of expressway

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Construction Annual Maintenance

Cement (tons) 1 million 50,000

Labor (hours) 100 million 5 million

Simplifying

assumptions

Construction

starts and

finishes this year

Maintenance

starts next year

Continues everyyear …


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Benefits of expressway

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Annual Benefits

Saved Time (hours) 5 million

Saved Lives 20

Simplifying assumptions Benefits starts this year

Continue every year …

E.g. 10 minutes per day x 150,000 commuters

x 200 commute days a year

= 300 million minutes a year

= 5 million hours a year


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Counting Secondary Benefits

Retailers at a shopping centre near an exit to newexpressway will gain profit. Should this profit be countedas a benefit?

Retailers at a shopping centre far from expressway willlose profit. Should this loss be counted as a reduction inbenefit?

If you count one, you should count the other; otherwiseexclude both

In a large full-employment economy, these secondarygains and losses will cancel out

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Task of CBA

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Cost Quantity Value Total

Cement 1 million tons

Labor 100 million hours

Maintenance

(starts next year)

Benefit (Yearly) Quantity Value Yearly Total

Saved time 5 million hours

Saved lives 20 lives

Total Cost over time:

Total Benefit over time:

Yearly:


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Three valuation problems in CBA

1. If market prices are available, do they reflect

costs and benefits correctly? If not, how to

adjust?

2. If market prices are not available, how to

measure costs and benefits?

3. How to compare costs and benefits

happening over a long period of time?

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Outline

1. Valuation with market prices

2. Valuation with no market prices

3. Valuation across Time4. Issues with CBA

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Value of inputs used (cement, labor) usually

have market prices available for valuation

For a public sector project, the correct measure

is the marginal opportunity cost to society of

using the input

• This may differ from the market price due to

market distortions

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Impact of imperfect competition

If cement is provided by a monopoly, then P >MC of cement production. Between the two (P,MC) which is better indicator of Opp. Cost to

society?• If monopoly doesn’t expand production at all,

opp. cost falls on ____________ P is betterindicator

• If monopoly expands production by the full 1million tons, then opp. cost falls on other

_______________MC is better indicator

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Impact of taxes and subsidies

Suppose cement production is done in a

competitive market, but is taxed, so P > MC.

Again, look at cement production response to

the project!

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Impact of Unemployment

If the economy has full employment, hiring aworker-hour for the project will reduce availablelabor for rest of economy

•

Thus, opp. cost of hiring one worker-hour =market wage rate

If the economy is in recession, hiring a worker-hourneed not be at the expense of the rest of economy

• Then, opp. cost of hiring one worker-hour = valueof one hour of leisure time for unemployed

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Common Mistake:Counting Job Creation as a Benefit

Politicians often tout the employment effects of

public sector projects

• “Build the expressway because 10,000 jobs

will be created!”

This implicitly values wages paid as a benefit of

the project!

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Impact of Large Scale Projects

A public sector project may be large enough to

change market prices

In that case, measurement of benefits and costs

will have to involve estimating price changes

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Task of CBA

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Cement 1 million tons

Labor 100 million hours

Maintenance

(starts next year)






Yearly:


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Outline



2.1 Value of Time

2.2 Value of Life

3. Valuation across Time

4. Issues with CBA

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Valuation with no market prices

Some costs (e.g. noise) and many benefits

(commuting time saved, lives saved) don’t have

market prices

• Other examples: defense, national prestige,

ecological diversity, aesthetics

An intangible is a benefit or cost for which there

is no obvious method of assigning a dollar value

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2.1 Value of Time

There are 3 valuation methods for intangibles

1. Use a measurable proxy

2. Ask people for their hypothetical responses to

different scenarios: Contingent Valuation3. Use actual market behavior to uncover peoples’

valuations: Revealed Preference

We apply the 3 methods to measuring the value ofcommuting time saved by the expressway project.

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Value of Time by Proxy

The idea here is that time is valuable because it

can be used to increase output

Thus, a proxy for the value of time would be the

wage rate of the average commuter

• E.g. wage rate is $10/hr

• Then saving 5 million hours has the value of

$50 million

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Value of Time by Contingent Valuation

Ask commuters in a survey:

“How much would you pay to cut your daily

commute by 10 minutes?”

• Easy to administer

• For some kind of intangibles (e.g. value of

preserving the Grand Canyon), surveys are the

only way to determine value

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Value of Time by Contingent Valuation

But answers may be highly sensitive to context, e.g.how the questions are asked (framing)

1. “How much would you pay to cut your daily

commute by 10 minutes?”2. “Considering the time you could spend with

your children, how much would you pay to cutyour daily commute by 10 minutes”

3. “How much would you pay to cut commutetime from Upper Thompson to City Hall by 10minutes?”

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Value of Time by Revealed Preference

Examine existing consumer behavior to tease outhow much they value time

• E.g. Time expended to get a discount

•Large corporate petrol stations sold petrol at lowerprice (by $0.395/gallon) than small independentpetrol stations

• On average, people were willing to wait 14.6 minutes

longer to buy 10.5 gallons of petrol at the largecorporate stations

• Value of 1 hour is thus $0.395 x 10.5 x 60/14.6 = $17

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Value of Time by Revealed Preference

E.g. compare prices of houses that differ only by

travel time to downtown

In practice, use regression analysis to control for

other salient differences

• This is called Hedonic Price Analysis

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Common Mistake: Double Counting

Property values along expressway exits will rise

But this merely reflects the value of savedcommute time, which is already being counted

in benefits

Thus, if rise in property value is separately

counted as a benefit, that is double-counting!

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2.2 Value of Life

Society cannot function if life is considered priceless• Should governments force hospitals to spend $1

million to extend the life of a 100-year-old patientto 101 years?

People do not behave as if life is priceless

• Driving is a risky activity, but people willingly do it

In CBA, a finite value of life is estimated, using the 3methods

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Value of a Life by Proxy

Use the expected value of lifetime earnings

Some uncomfortable implications

• Mens’ lives are more valuable than womens’

• The younger you are the more valuable your life

• High earner’s life is more valuable

• Life in UK is dear; life in India is cheap

• You have no value outside your working capacity!

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Value of a life by Contingent Valuation

Ask commuters in a survey: “How much would

you pay to cut your probability of death by from

2 in 10,000 to 1 in 10,000?”

Again, framing matters

• E.g. People might pay more to avoid gruesome

deaths

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Value of a Life by Revealed Preference

Look at how much consumers actually spend on

safety devices such as car airbags

• E.g. airbag costs $350 but lowers Pr(death) by

1:10,000, then value of life is $3.5 million

• Do consumers really understand these risks

when they are making purchase decisions?

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Look at compensating differential in wagesobtained from doing risky jobs

• E.g. job in oilrig raises Pr(death) by 0.1% but pays

$10,000 more annually, then value of life is $10

million

• People who take on dangerous jobs may be

more risk-loving than the general population

• Do workers fully understand the risks they

face?

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Estimates of “Value of a Statistical Life”

0100020003000400050006000

700080009000

Estimated Value of a Statistical Life by Country

(1995 USD)

VSL

32Source: Miller (2000)


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Estimates of

“Value of a

StatisticalLife”

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Source: Viscusi and Aldy (2003)

http://www.nber.org/papers/w9487.pdfhttp://www.nber.org/papers/w9487.pdf


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Task of CBA

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Cement 1 million tons $1,000/ton $1 billion

Labor 100 million hours $10/hr $1 billion

Maintenance

(starts next year)






Yearly: $100 million


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Outline



3. Valuation across Time3.1 Discounting and Present Value

3.2 What discount rate to use?

4. Issues with CBA

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3.1 Discounting and Present Value

Suppose the market interest rate is 5% per year

The Present Value (PV) of “$110 in one year’s time”

= $___ today that will yield $110 in one year’s time,• Ans: $110 / 1.05 = $104.76

The process of converting a future value into its PVis called discounting, and the interest rate used iscalled the discount rate

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Using PV to compare $ values over time

Is $100 today better, or $110 in two year’s time?

PV of “$110 in two year’s time”

= $110 / 1.052

= $99.77

$100 today is better, since $99.77 today wouldyield $110 two years from now, and $100 today

is certainly better than $99.77 today

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Discounting Benefits and Costs

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(benefits) =

(+)

(+) ⋯

(+)

(costs) =

(+)

(+) ⋯

(+)

A project provides benefits {B0, B1, B2 …. BT-1, BT}and costs {C0, C1, C2 …. CT-1, CT}

Assume for simplicity that the discount rate r isconstant across periods


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Discounting perpetual streams

For a perpetual stream of constant cost C,

starting next period (i.e. C0 = 0), PV is given by:

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(costs) = 0 ( 1 )

( 1 )2

( 1 )

⋯

=

( 1 ) 1

1

( 1 )

1

( 1 )2 ⋯

=

( 1 )

1

=


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E.g. Discounting for expressway project

Cost of maintenance is constant $100 million

(i.e. $108) per year, starting next year

Suppose discount rate is constant 7% per year

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= 0 $108

(1 0.07)

$108

(1 0.07)2

$108

(1 0.07) ⋯

≈ $1.43 billion

=

$108

0.07


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Task of CBA

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Cement 1 million tons $1,000/ton $1 billion

Labor 100 million hours $10/hr $1 billion

Maintenance

(starts next year)


Saved time 5 million hours $20/hr $100 million

Saved lives 20 lives $8 million/life $160 million



Yearly: $100 million


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3.2 What discount rate to use?

The Social Discount Rate (SDR) should reflect

the social opportunity cost of funds invested in

the project

There is no consensus on what constitutes the

appropriate SDR

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Using private sector rate of return

One approach: treat funds as being taken away

from private sector, affecting either investment

or current consumption

• If funds are taken from investment, then SDR

= B4-tax return on investment projects

• If funds are taken from consumption, then

SDR = after-tax return on investment projects

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Should SDR be lower thanprivate sector rate of return?

• Paternalism: people may be myopic they

over-discount

• For long term projects, future generations

aren’t well-represented by market rates

• See Seidman Ch 4 p. 90 for discussion about

Stern Review on the Economics of Climate

Change

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Outline



3. Valuation across Time

4. Issues with CBA

4.1 Decision Rules

4.2 Distributional concerns4.3 Dealing with Uncertainty

4.4 To use or not to use CBA

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4.1 Decisions Rules

Net Present Value (preferred way)

Internal Rate of Return

Benefit-Cost Ratio

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Net Present Value

The Net Present Value of the project is given by

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= benefits − costs

The NPV criteria(1) Project should be done only if NPV > 0

(2) Between two mutually exclusive projects,

choose the one with higher NPV


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Internal Rate of Return

The Internal Rate of Return ρ = discount rate that makesNPV of a project = 0

The IRR criteria

(1) Project should be done only if ρ > r(2) Between two mutually exclusive projects, choose theone with higher ρ

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Project Benefits(1 year later)

Costs(today)

NPV(r = 7%)

IRR

A $110 $100 $2.80

B $220 $200 $5.60


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Benefit-Cost Ratio

The benefit-cost ratio = PV(benefits) / PV(costs)

The BCR criteria

(1) Project should be done only if BCR > 1

(2) if two projects are mutually exclusive, choosethe project with higher BCR

Problem: Suppose project results in $100 damageto environment

• Count as cost BCR denominator ↑

• Count as benefit BCR numerator ↓49


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4.2 Distributional Concerns

CBA is not concerned with the project’s

distribution of benefits and costs.

• If NPV is positive, you can potentially have

winners compensate losers, and still havewinners be better off

• Hicks-Kaldor Criterion: project is admissible if

it allows for a potential Pareto Improvement (which is satisfied if NPV is positive)

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Distributional Concerns

In principle, one can modify CBA to weigh

different people’s benefits and costs differently

• E.g. a $1 benefit to a poor person = $10

benefit to a rich person

But should CBA be thus modified? Or should

governments follow Hicks-Kaldor?

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4.3 Dealing with Uncertainty

If there is uncertainty, must make adjustments

to CBA

• Compute costs and benefits under alternative

scenarios

• Compute certainty equivalents (RG Chapter 8

Appendix, not required)

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4.4 To Use or Not to Use CBA

• Not popular with bureaucrats and politicianspushing their pet projects

• Not popular with environmentalists and

consumer advocates who do not accept valuationof intangibles

• US Clean Air Act, Endangered Species Actexplicitly prohibits CBA!

• Even when used, rarely the sole determinant• In Singapore, CBA is sometimes done, but almost

never published

topic 4 cost benefit analysis (with page 41)

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